Finite difference modelling, Fourier analysis, and stability

Peter Malcolm Manning, Gary F. Margrave

This paper uses Fourier analysis to present conclusions about stability and dispersion in finite difference modelling. The most elementary finite difference model is presented, one dimension in space with second order accuracy in space and time. For this one spatial dimension case formulae are derived to correct for the dispersion caused by finite grid sampling. The conclusions drawn are compatible with other discussions of stability in one dimension.